Decimal Operations

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Answer Key & Explanations

Decimal Operations · Grade 5 · Worksheet 3

1. Compare: 9.408 __ 9.480 Answer: < Solution: Write the numbers vertically, aligning the decimal points: 9.408 9.480 Compare the whole number parts: both are 9, so they are equal. Compare the tenths place: both are 4, so they are equal.
   Full step-by-step solution

   Step 1: Write the numbers vertically, aligning the decimal points: 9.408 9.480 Step 2: Compare the whole number parts: both are 9, so they are equal. Step 3: Compare the tenths place: both are 4, so they are equal. Step 4: Compare the hundredths place: 0 in 9.408 and 8 in 9.480. Since 0 < 8, 9.408 is less than 9.480. Step 5: Therefore, 9.408 < 9.480. The answer is <.

2. Emma is comparing the lengths of three ribbons for her art project. The red ribbon is 1.245 meters long, the blue ribbon is 1.254 meters long, and the green ribbon is 1.24 meters long. Which ribbon is the longest? Answer: A. Blue ribbon Solution: Write all three lengths with the same number of decimal places: Red = 1.245, Blue = 1.254, Green = 1.240 Compare the ones place: All have 1, so move to tenths place Compare the tenths place: All have 2, so move to hundredths place Compare the hundredths place: Red has 4, Blue has 5, Green has 4…
   Full step-by-step solution

   Step 1: Write all three lengths with the same number of decimal places: Red = 1.245, Blue = 1.254, Green = 1.240 Step 2: Compare the ones place: All have 1, so move to tenths place Step 3: Compare the tenths place: All have 2, so move to hundredths place Step 4: Compare the hundredths place: Red has 4, Blue has 5, Green has 4 Step 5: Since Blue has 5 hundredths while Red and Green have 4 hundredths, Blue is the longest Step 6: The blue ribbon (1.254 m) is longer than the red ribbon (1.245 m) and the green ribbon (1.240 m) The correct answer is Blue ribbon.

3. A rectangular prism-shaped shipping container has dimensions of 2.5 meters by 3.8 meters by 4.2 meters. What is the volume of this container in cubic meters? Answer: 39.9 Solution: Identify the formula for volume of a rectangular prism: Volume = length × width × height Substitute the given dimensions: Volume = 2.5 × 3.8 × 4.2 First multiply 2.5 × 3.8 = 9.5 Then multiply 9.5 × 4.2 = 39.9 The volume is 39.9 cubic meters
   Full step-by-step solution

   Step 1: Identify the formula for volume of a rectangular prism: Volume = length × width × height Step 2: Substitute the given dimensions: Volume = 2.5 × 3.8 × 4.2 Step 3: First multiply 2.5 × 3.8 = 9.5 Step 4: Then multiply 9.5 × 4.2 = 39.9 Step 5: The volume is 39.9 cubic meters

4. Mere is recording the rainfall amounts in her garden for three days. On Monday, 4.038 centimeters of rain fell. On Tuesday, 4.083 centimeters fell. On Wednesday, 4.38 centimeters fell. Write the rainfall amounts in order from least to greatest. Answer: 4.038, 4.083, 4.38 Solution: Write all three numbers with the same number of decimal places to make comparison easier: Monday: 4.038, Tuesday: 4.083, Wednesday: 4.380. Compare the whole number parts: all are 4, so they are the same.
   Full step-by-step solution

   Step 1: Write all three numbers with the same number of decimal places to make comparison easier: Monday: 4.038, Tuesday: 4.083, Wednesday: 4.380. Step 2: Compare the whole number parts: all are 4, so they are the same. Step 3: Compare the tenths place: Monday has 0, Tuesday has 0, Wednesday has 3. Since 0 < 3, Wednesday is the greatest so far, and Monday and Tuesday are smaller. Step 4: Compare Monday and Tuesday. They both have 0 tenths, so move to the hundredths place. Monday has 3 hundredths, Tuesday has 8 hundredths. Since 3 < 8, Monday is smaller than Tuesday. Step 5: So from least to greatest: Monday (4.038), Tuesday (4.083), Wednesday (4.38). The answer is 4.038, 4.083, 4.38.

5. 0.875 + 0.125 = ? Answer: 1.000 Solution: Write the problem vertically, aligning the decimal points: 0.875 + 0.125 Add the thousandths place: 5 + 5 = 10. Write down 0 in the thousandths place and carry over 1 to the hundredths place.
   Full step-by-step solution

   Step 1: Write the problem vertically, aligning the decimal points: 0.875 + 0.125 -------- Step 2: Add the thousandths place: 5 + 5 = 10. Write down 0 in the thousandths place and carry over 1 to the hundredths place. Step 3: Add the hundredths place: 7 + 2 = 9, plus the carried over 1 = 10. Write down 0 in the hundredths place and carry over 1 to the tenths place. Step 4: Add the tenths place: 8 + 1 = 9, plus the carried over 1 = 10. Write down 0 in the tenths place and carry over 1 to the ones place. Step 5: Add the ones place: 0 + 0 = 0, plus the carried over 1 = 1. Step 6: The final answer is 1.000, which can be written simply as 1.

6. 0.875 × 2.4 = ? Answer: 2.1 Solution: Multiply 0.875 × 2.4 as if they were whole numbers: 875 × 24 875 × 20 = 17,500 875 × 4 = 3,500 Add the partial products: 17,500 + 3,500 = 21,000 Count the decimal places: 0.875 has 3 decimal places, 2.4 has 1 decimal place, so total is 4 decimal places Place the decimal point in 21,000 to get 4…
   Full step-by-step solution

   Step 1: Multiply 0.875 × 2.4 as if they were whole numbers: 875 × 24 Step 2: 875 × 20 = 17,500 Step 3: 875 × 4 = 3,500 Step 4: Add the partial products: 17,500 + 3,500 = 21,000 Step 5: Count the decimal places: 0.875 has 3 decimal places, 2.4 has 1 decimal place, so total is 4 decimal places Step 6: Place the decimal point in 21,000 to get 4 decimal places: 2.1000 Step 7: Simplify: 2.1000 = 2.1 The answer is 2.1.

7. Aroha is comparing the weights of three different fruits at the market. A pumpkin weighs 3.507 kilograms, a watermelon weighs 3.57 kilograms, and a cantaloupe weighs 3.075 kilograms. Which fruit is the heaviest? Answer: 3.57 Solution: Write all three weights with the same number of decimal places for easy comparison: Pumpkin: 3.507 kg Watermelon: 3.570 kg (add a zero to the thousandths place) Cantaloupe: 3.075 kg Compare the whole number parts.
   Full step-by-step solution

   Step 1: Write all three weights with the same number of decimal places for easy comparison: Pumpkin: 3.507 kg Watermelon: 3.570 kg (add a zero to the thousandths place) Cantaloupe: 3.075 kg Step 2: Compare the whole number parts. All have 3, so move to the tenths place. Step 3: Compare the tenths place: Pumpkin: 5 tenths Watermelon: 5 tenths Cantaloupe: 0 tenths Cantaloupe is smaller, so it is not the heaviest. Step 4: Compare the hundredths place for Pumpkin and Watermelon: Pumpkin: 0 hundredths Watermelon: 7 hundredths 7 hundredths is greater than 0 hundredths. Step 5: Since Watermelon has 7 hundredths and Pumpkin has 0 hundredths, the watermelon is heavier. The heaviest fruit is the watermelon, weighing 3.57 kilograms.